Work, Energy and Momentum Notes 3 – Momentum and Collisions
Transcript of Work, Energy and Momentum Notes 3 – Momentum and Collisions
Work,EnergyandMomentumNotes
3–MomentumandCollisions
Momentumisaquantityofmotionthatdependsonboththemassandvelocityoftheobjectinquestion.
Theunitsofmomentumare:
Remember:Momentumisa_________quantity,withthesamesignasitsvelocity.Aswithanyvectoryoucanassignanydirectionaspositiveandtheoppositeasnegative,butasconventionwewillrefertouportotherightaspositiveanddownortotheleftasnegative.
Example:Abaseballpitcherhurlsaballat32m/s.Thebattercrushesitandtheballleavesthebatat48m/s.Whatwastheball’schangeinmomentum?
RememberthatmomentumisaVECTORwhichmeans:
Impulse:
Recallthatmomentumistheproductof_________and___________.Sincewewillnotbedealingwithchangingmasses,wecandefineanobject’schangeinmomentumas:
Wheneveranetforceactsonabody,anaccelerationresultsandsoitsmomentummustchange.
Derivation:
Let’strytounderstandhowforcesrelatetochangesinmomentumwithafewexamples. Astudentjumpsoffadesk.Whentheylandtheybendtheirkneesonimpact.Whydoesthishelppreventsomeseriousdamagetotheirknees?
Coachesformanysportssuchasbaseball,tennisandgolfcanoftenbeheardtellingtheirathletesto“followthrough”withtheirswing.Whyisthissoimportant?
Conventionalwisdomsuggeststhatcarsshouldbemadetoughandrigidtopreventinjuryduringacollision,howevernewervehiclesareallbuiltwithlargecrumplezones.Why?
Abeanbagandahighbounceballofequalmassesaredroppedfromthesameheight.Thebeanbagisbroughttoastopinthesametimethattheballisincontactwiththefloor.Whichoneexertsagreateraverageforceonthefloor?
TheLawofConservationofMomentumMomentumisausefulquantitybecauseinaclosedsystemitisalwaysconserved.Thismeansthatinanycollision,thetotalmomentumbeforethecollisionmustequalthetotalmomentumafterthecollision.
Therearetwowaysofthinkingabouttheconservationofmomentum:
(1)
(2)
ExampleA115kgfullbackrunningat4.0m/sEastisstoppedin0.75sbyahead-ontackle.Calculate
a) theimpulsefeltbythefullback.b) theimpulsefeltbythetackler.c) theaveragenetforceexertedonthetackler.
ExampleA1250kgcartravelingeastat25m/sturnsduenorthandcontinuesonat15m/s.Whatwastheimpulseofthecarexertedwhileturningthecorner?
Collisionscanbegroupedintotwocategories,
ElasticCollisions:
InelasticCollisions:
Inrealitycollisionsaregenerallysomewhereinbetweenperfectlyelasticandperfectlyinelastic.Asamatteroffact,itisimpossibleforamacroscopiccollisiontoeverbeperfectlyelastic.Perfectlyelasticcollisionscanonlyoccurattheatomicorsubatomiclevel.Whycan’tmacroscopiccollisioneverbetrulyelastic?
Inelastic
Elastic
Explosions
A9500kgcabooseisatrestonsometracks.An11000kgenginemovingeastat12.0m/scollideswithitandtheysticktogether.Whatisthevelocityofthetraincarsafterthecollision?
Afirecrackerisplacedinapumpkinwhichexplodesinintoexactlytwopieces.Thefirstpiecehasamassof2.2kgandfliesdueeastat26m/s.Thesecondchunkheadsduewestat34m/s.Whatwastheinitialmassofthepumpkin?
Tworugbyplayersofequalmasscollideheadonwhiletravelingatthesamespeed.Whatistheirfinalspeed?Ismomentumconserved?Isenergyconserved?Iskineticenergyconserved?
Aprotontravelingat2x103m/scollideswithastationaryprotonandcomestorest.Whatisthefinalspeedoftheotherproton?Iskineticenergyconserved?
Analphaparticlehasamassapproximately4timeslargerthanaproton.Aprotontravelingtotherightat3200m/sstrikesastationaryalphaparticleitreboundsat1920m/s.Whatisthefinalspeedofthealphaparticle?
Work,EnergyandMomentumNotes
4–Collisionsin2-D
Whendealingwithcollisionsin2-dimensionsitisimportanttorememberthatmomentumisavectorwithmagnitudeanddirection.Whenfindingthetotalmomentumwehavetodo:
Collisionsnotat90o(becauselifeisneverthateasy…):
A4.0kgbowlingballismovingeastatanunknownvelocitywhenitcollideswitha6.1kgfrozencantaloupeatrest.Afterthecollision,thebowlingballistravelingatavelocityof2.8m/s32oNofEandthecantaloupeistravelingatavelocityof1.5m/s41oSofE.Whatwastheinitialvelocityofthebowlingball?
ComponentMethodWeneedtobreakthefinalmomentaofthetwoobjectsintoxandycomponents:
Before After
Collisions at 90o: A 750 kg Peugeot travelling at 21 m/s West collides with a 680 kg Fiat travelling at 18 m/s South. If the two cars become entwined what is their total final velocity?
Remember that it is momentum that is conserved, so we need to add the ______________ NOT _____________